Most Republican reforms involve shifting away from employer-based health insurance -- replacing the massive tax breaks for companies with subsidies to individuals and families to purchase coverage on their own.

In other words,

Healthcare will cost less when you disband pooling of risk and bargaining power and instead have people deal with large insurance companies on an individual basis.

That is the Republican fantasy which posits that markets are perfect. That all markets operate as if there are many suppliers and many buyers of a standard product. And that such "ideal pricing" must be borne by the individual even if it is unaffordable for certain (random) health conditions.

Anything in scarce supply that is just "subsidized" just raises the price by the amount of the subsidy.

Section 8 housing, Medicare Part D, the mortgage interest deduction, it's all the same thing, the money from the government ends up in the pockets of the respective industry (landlords, big pharma, bankers, respectively).